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        <h1>Main</h1>
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        <span class="name">Main</span><span class="result"> extends <span name="scala.App" class="extype">App</span> with <a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></span>
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              <h3>Type Members</h3>
              <ol><li visbl="pub" name="giantnums.GiantRationals#PQ" data-isabs="false">
      <a id="PQ:(AlgT, AlgT)"></a>
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      <span class="symbol">
        <span class="name">PQ</span><span class="result"> = (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
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              <h3>Value Members</h3>
              <ol><li visbl="pub" name="scala.AnyRef#!=" data-isabs="false">
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        <span class="modifier">final </span>
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      <span class="symbol">
        <span class="name" title="gt4s: $bang$eq">!=</span><span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
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        <span class="kind">def</span>
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      <span class="symbol">
        <span class="name" title="gt4s: $bang$eq">!=</span><span class="params">(<span name="arg0">arg0: <span name="scala.Any" class="extype">Any</span></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
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        <span class="modifier">final </span>
        <span class="kind">def</span>
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      <span class="symbol">
        <span class="name" title="gt4s: $hash$hash">##</span><span class="params">()</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
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      <a id="==(AnyRef):Boolean"></a>
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      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name" title="gt4s: $eq$eq">==</span><span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
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      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name" title="gt4s: $eq$eq">==</span><span class="params">(<span name="arg0">arg0: <span name="scala.Any" class="extype">Any</span></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
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    </li><li visbl="pub" name="giantnums.GiantNaturals#EQ" data-isabs="false">
      <a id="EQ:Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">EQ</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
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      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
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      <a id="FIVE:V"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
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      <span class="symbol">
        <span class="name">FIVE</span><span class="result">: <a name="giantnums.V" class="extype" href="V.html">V</a></span>
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      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
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      <a id="FOUR:W"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">FOUR</span><span class="result">: <a name="giantnums.W" class="extype" href="W.html">W</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#GT" data-isabs="false">
      <a id="GT:Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">GT</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#LT" data-isabs="false">
      <a id="LT:Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">LT</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
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      <a id="ONE:V"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">ONE</span><span class="result">: <a name="giantnums.V" class="extype" href="V.html">V</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
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      <a id="SEVEN:V"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">SEVEN</span><span class="result">: <a name="giantnums.V" class="extype" href="V.html">V</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
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      <a id="SIX:W"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">SIX</span><span class="result">: <a name="giantnums.W" class="extype" href="W.html">W</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#THREE" data-isabs="false">
      <a id="THREE:V"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">THREE</span><span class="result">: <a name="giantnums.V" class="extype" href="V.html">V</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#TWO" data-isabs="false">
      <a id="TWO:W"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">TWO</span><span class="result">: <a name="giantnums.W" class="extype" href="W.html">W</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#add" data-isabs="false">
      <a id="add(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">add</span><span class="params">(<span name="u">u: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="v">v: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">addition operation on binary trees, corresponding
to addition on N
- termination proof obvious: structural recursion
</p><div class="fullcomment"><div class="comment cmt"><p>addition operation on binary trees, corresponding
to addition on N
- termination proof obvious: structural recursion
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="prt" name="scala.App#args" data-isabs="false">
      <a id="args:Array[String]"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">args</span><span class="result">: <span name="scala.Array" class="extype">Array</span>[String]</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>protected </dd><dt>Definition Classes</dt><dd>App</dd></dl></div>
    </li><li visbl="pub" name="scala.Any#asInstanceOf" data-isabs="false">
      <a id="asInstanceOf[T0]:T0"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">asInstanceOf</span><span class="tparams">[<span name="T0">T0</span>]</span><span class="result">: T0</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>Any</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#bits" data-isabs="false">
      <a id="bits:Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">bits</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.AlgT#cI" data-isabs="false">
      <a id="cI(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">cI</span><span class="params">(<span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">constructor seen as adding a 1 digit to the
least significant end of a bijective base-2
number
</p><div class="fullcomment"><div class="comment cmt"><p>constructor seen as adding a 1 digit to the
least significant end of a bijective base-2
number
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.AlgT#cO" data-isabs="false">
      <a id="cO(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">cO</span><span class="params">(<span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">constructor seen as adding a 0 digit to the
least significant end of a bijective base-2
number
</p><div class="fullcomment"><div class="comment cmt"><p>constructor seen as adding a 0 digit to the
least significant end of a bijective base-2
number
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.AlgT#cS" data-isabs="false">
      <a id="cS(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">cS</span><span class="params">(<span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">constructor seen as adding 1 to a
bijective base-2 number, avg.</p><div class="fullcomment"><div class="comment cmt"><p>constructor seen as adding 1 to a
bijective base-2 number, avg.
effort O(1) ~ avg. number of 1s a
number ends with
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></dd></dl></div>
    </li><li visbl="prt" name="scala.AnyRef#clone" data-isabs="false">
      <a id="clone():AnyRef"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">clone</span><span class="params">()</span><span class="result">: AnyRef</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>protected[<a name="java.lang" class="extype" href="../java/lang/package.html">lang</a>] </dd><dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#cmp" data-isabs="false">
      <a id="cmp(AlgT,AlgT):Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">cmp</span><span class="params">(<span name="u">u: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="v">v: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">comparaison function returning LT,EQ,GT
</p><div class="fullcomment"><div class="comment cmt"><p>comparaison function returning LT,EQ,GT
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.AlgT#dI" data-isabs="false">
      <a id="dI(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">dI</span><span class="params">(<span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">extractor, seen as removing a 1 digit from the
least significant end of a bijective base-2
number
</p><div class="fullcomment"><div class="comment cmt"><p>extractor, seen as removing a 1 digit from the
least significant end of a bijective base-2
number
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.AlgT#dO" data-isabs="false">
      <a id="dO(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">dO</span><span class="params">(<span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">extractor, seen as removing a 0 digit from the
least significant end of a bijective base-2
number
</p><div class="fullcomment"><div class="comment cmt"><p>extractor, seen as removing a 0 digit from the
least significant end of a bijective base-2
number
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.AlgT#dS" data-isabs="false">
      <a id="dS(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">dS</span><span class="params">(<span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">extractor, seen as subtracting 1 from a
bijective base-2 number, when possible,
i.</p><div class="fullcomment"><div class="comment cmt"><p>extractor, seen as subtracting 1 from a
bijective base-2 number, when possible,
i.e. when not the empty sequence</p><p>effort O(1) ~ avg. number of 1s a
number ends with
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#db" data-isabs="false">
      <a id="db(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">db</span><span class="params">(<span name="t">t: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.App#delayedInit" data-isabs="false">
      <a id="delayedInit(⇒ Unit):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">delayedInit</span><span class="params">(<span name="body">body: ⇒ <span name="scala.Unit" class="extype">Unit</span></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>App → DelayedInit</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#diadicValuation" data-isabs="false">
      <a id="diadicValuation(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">diadicValuation</span><span class="params">(<span name="x">x: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">smallest exponent of 2 that divides x
</p><div class="fullcomment"><div class="comment cmt"><p>smallest exponent of 2 that divides x
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#div" data-isabs="false">
      <a id="div(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">div</span><span class="params">(<span name="x">x: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="y">y: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">division
</p><div class="fullcomment"><div class="comment cmt"><p>division
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#div_and_rem" data-isabs="false">
      <a id="div_and_rem(AlgT,AlgT):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">div_and_rem</span><span class="params">(<span name="x">x: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="y">y: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">division with remainder operation on binary trees, corresponding
to the same on N
</p><div class="fullcomment"><div class="comment cmt"><p>division with remainder operation on binary trees, corresponding
to the same on N
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#dual" data-isabs="false">
      <a id="dual(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">dual</span><span class="params">(<span name="t">t: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">the dual represents a number in which Os and Is are flipped
it is constant time with our representation</p><div class="fullcomment"><div class="comment cmt"><p>the dual represents a number in which Os and Is are flipped
it is constant time with our representation</p><p>a constant time operation</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#eq" data-isabs="false">
      <a id="eq(AnyRef):Boolean"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">eq</span><span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#equals" data-isabs="false">
      <a id="equals(Any):Boolean"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">equals</span><span class="params">(<span name="arg0">arg0: <span name="scala.Any" class="extype">Any</span></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef → Any</dd></dl></div>
    </li><li visbl="pub" name="scala.App#executionStart" data-isabs="false">
      <a id="executionStart:Long"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">executionStart</span><span class="result">: <span name="scala.Long" class="extype">Long</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>App</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#exp2" data-isabs="false">
      <a id="exp2(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">exp2</span><span class="params">(<span name="t">t: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">exponent of 2 : a constant avg.</p><div class="fullcomment"><div class="comment cmt"><p>exponent of 2 : a constant avg. time operation
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#fermat" data-isabs="false">
      <a id="fermat(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">fermat</span><span class="params">(<span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">n-the Fermat number
</p><div class="fullcomment"><div class="comment cmt"><p>n-the Fermat number
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="prt" name="scala.AnyRef#finalize" data-isabs="false">
      <a id="finalize():Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">finalize</span><span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>protected[<a name="java.lang" class="extype" href="../java/lang/package.html">lang</a>] </dd><dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#fraq2pq" data-isabs="false">
      <a id="fraq2pq((BigInt, BigInt)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">fraq2pq</span><span class="params">(<span name="nd">nd: (BigInt, BigInt)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#fromT" data-isabs="false">
      <a id="fromT(AlgT):Q"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">fromT</span><span class="params">(<span name="t">t: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Signed Rationals from trees seen as natural numbers
</p><div class="fullcomment"><div class="comment cmt"><p>Signed Rationals from trees seen as natural numbers
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#gcd" data-isabs="false">
      <a id="gcd(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">gcd</span><span class="params">(<span name="x">x: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="y">y: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">greatest common divisor
</p><div class="fullcomment"><div class="comment cmt"><p>greatest common divisor
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#getClass" data-isabs="false">
      <a id="getClass():java.lang.Class[_]"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">getClass</span><span class="params">()</span><span class="result">: java.lang.Class[_]</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef → Any</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#hashCode" data-isabs="false">
      <a id="hashCode():Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">hashCode</span><span class="params">()</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef → Any</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#hf" data-isabs="false">
      <a id="hf(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">hf</span><span class="params">(<span name="x">x: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">half of an even number
</p><div class="fullcomment"><div class="comment cmt"><p>half of an even number
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.Any#isInstanceOf" data-isabs="false">
      <a id="isInstanceOf[T0]:Boolean"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">isInstanceOf</span><span class="tparams">[<span name="T0">T0</span>]</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>Any</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#lastTime" data-isabs="false">
      <a id="lastTime:Long"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">var</span>
      </span>
      <span class="symbol">
        <span class="name">lastTime</span><span class="result">: <span name="scala.Long" class="extype">Long</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#lcm" data-isabs="false">
      <a id="lcm(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">lcm</span><span class="params">(<span name="x">x: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="y">y: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">least common multiplier
</p><div class="fullcomment"><div class="comment cmt"><p>least common multiplier
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#lucasLehmer" data-isabs="false">
      <a id="lucasLehmer(AlgT):Boolean"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">lucasLehmer</span><span class="params">(<span name="p">p: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt"> Lucas-Lehmer fast primality test for Mersenne numbers
</p><div class="fullcomment"><div class="comment cmt"><p> Lucas-Lehmer fast primality test for Mersenne numbers
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.App#main" data-isabs="false">
      <a id="main(Array[String]):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">main</span><span class="params">(<span name="args">args: <span name="scala.Array" class="extype">Array</span>[String]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>App</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#mersenne" data-isabs="false">
      <a id="mersenne(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">mersenne</span><span class="params">(<span name="p">p: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">a Mersenne number associated to prime p
</p><div class="fullcomment"><div class="comment cmt"><p>a Mersenne number associated to prime p
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#mersenne45" data-isabs="false">
      <a id="mersenne45:AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">mersenne45</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">the largest known prime number up to december 2012,
a Mersenne numbe
</p><div class="fullcomment"><div class="comment cmt"><p>the largest known prime number up to december 2012,
a Mersenne numbe
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#mersennePrimeExps" data-isabs="false">
      <a id="mersennePrimeExps(AlgT):List[AlgT]"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">mersennePrimeExps</span><span class="params">(<span name="limit">limit: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <span name="scala.collection.immutable.List" class="extype">List</span>[<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">generates the exponents of Mersenne primes up to limit
</p><div class="fullcomment"><div class="comment cmt"><p>generates the exponents of Mersenne primes up to limit
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#mersennePrimes" data-isabs="false">
      <a id="mersennePrimes(AlgT):List[AlgT]"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">mersennePrimes</span><span class="params">(<span name="expLimit">expLimit: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <span name="scala.collection.immutable.List" class="extype">List</span>[<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">generates the actual Mersenne primes for exponents
up to limit
</p><div class="fullcomment"><div class="comment cmt"><p>generates the actual Mersenne primes for exponents
up to limit
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#millerRabin" data-isabs="false">
      <a id="millerRabin(AlgT,AlgT):Boolean"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">millerRabin</span><span class="params">(<span name="k">k: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Miller-Rabin primality test for n
with (1/4)^k chances of being wrong
</p><div class="fullcomment"><div class="comment cmt"><p>Miller-Rabin primality test for n
with (1/4)^k chances of being wrong
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#millerRabinStep" data-isabs="false">
      <a id="millerRabinStep(AlgT,AlgT):Boolean"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">millerRabinStep</span><span class="params">(<span name="a">a: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="n">n: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">deterministic step in Miller-Rabin primality test
</p><div class="fullcomment"><div class="comment cmt"><p>deterministic step in Miller-Rabin primality test
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#millerTest" data-isabs="false">
      <a id="millerTest(BigInt):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">millerTest</span><span class="params">(<span name="n">n: BigInt</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#modPow" data-isabs="false">
      <a id="modPow(AlgT,AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">modPow</span><span class="params">(<span name="b">b: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="exp">exp: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="m">m: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">computes (b^exp) modulo m
</p><div class="fullcomment"><div class="comment cmt"><p>computes (b^exp) modulo m
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#mul" data-isabs="false">
      <a id="mul(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">mul</span><span class="params">(<span name="u">u: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="v">v: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">multiplication operation on binary trees, corresponding
to multiplication on N
</p><div class="fullcomment"><div class="comment cmt"><p>multiplication operation on binary trees, corresponding
to multiplication on N
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#n2t" data-isabs="false">
      <a id="n2t(BigInt):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">n2t</span><span class="params">(<span name="n">n: BigInt</span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">converts a BigInt representing a natural number
to its bijectively related tree representation
</p><div class="fullcomment"><div class="comment cmt"><p>converts a BigInt representing a natural number
to its bijectively related tree representation
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#nat2rat" data-isabs="false">
      <a id="nat2rat(BigInt):Q"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">nat2rat</span><span class="params">(<span name="n">n: BigInt</span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">bijection from BigInt natural numbers to
tree-represented Signed Rationals
</p><div class="fullcomment"><div class="comment cmt"><p>bijection from BigInt natural numbers to
tree-represented Signed Rationals
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#ne" data-isabs="false">
      <a id="ne(AnyRef):Boolean"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">ne</span><span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#notify" data-isabs="false">
      <a id="notify():Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">notify</span><span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#notifyAll" data-isabs="false">
      <a id="notifyAll():Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">notifyAll</span><span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#op1" data-isabs="false">
      <a id="op1((AlgT) ⇒ AlgT,BigInt):BigInt"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">op1</span><span class="params">(<span name="f">f: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>) ⇒ <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="x">x: BigInt</span>)</span><span class="result">: BigInt</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#op2" data-isabs="false">
      <a id="op2((AlgT, AlgT) ⇒ AlgT,BigInt,BigInt):BigInt"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">op2</span><span class="params">(<span name="f">f: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>) ⇒ <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="x">x: BigInt</span>, <span name="y">y: BigInt</span>)</span><span class="result">: BigInt</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#optest1" data-isabs="false">
      <a id="optest1(String,(AlgT) ⇒ AlgT,BigInt):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">optest1</span><span class="params">(<span name="opname">opname: String</span>, <span name="f">f: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>) ⇒ <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="x">x: BigInt</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#optest2" data-isabs="false">
      <a id="optest2(String,(AlgT, AlgT) ⇒ AlgT,BigInt,BigInt):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">optest2</span><span class="params">(<span name="opname">opname: String</span>, <span name="f">f: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>) ⇒ <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="x">x: BigInt</span>, <span name="y">y: BigInt</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#perfect" data-isabs="false">
      <a id="perfect(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">perfect</span><span class="params">(<span name="p">p: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">an (even) perfect number associated to prime p,
i.</p><div class="fullcomment"><div class="comment cmt"><p>an (even) perfect number associated to prime p,
i.e. number such that the sum of its proper
divisors equals it</p><p>surprisingly, computing this is constant time
operation
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#perfect45" data-isabs="false">
      <a id="perfect45:AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">perfect45</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">the largest known perfect number up to december 2012,
derived from the largest known Mersenne prime
</p><div class="fullcomment"><div class="comment cmt"><p>the largest known perfect number up to december 2012,
derived from the largest known Mersenne prime
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#pow" data-isabs="false">
      <a id="pow(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pow</span><span class="params">(<span name="u">u: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="v">v: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">power operation on binary trees, corresponding
to u at exponent v on N
</p><div class="fullcomment"><div class="comment cmt"><p>power operation on binary trees, corresponding
to u at exponent v on N
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pq2fraq" data-isabs="false">
      <a id="pq2fraq((AlgT, AlgT)):(BigInt, BigInt)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pq2fraq</span><span class="params">(<span name="nd">nd: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (BigInt, BigInt)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pq2t" data-isabs="false">
      <a id="pq2t((AlgT, AlgT)):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pq2t</span><span class="params">(<span name="uv">uv: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">fuses back into a &quot;natural number&quot;,
representing the path in the Calkin-Wilf tree,
a pair of co-prime natural numbers representing
the (numerator,denominator) of a positive rational number
</p><div class="fullcomment"><div class="comment cmt"><p>fuses back into a &quot;natural number&quot;,
representing the path in the Calkin-Wilf tree,
a pair of co-prime natural numbers representing
the (numerator,denominator) of a positive rational number
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqadd" data-isabs="false">
      <a id="pqadd((AlgT, AlgT),(AlgT, AlgT)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqadd</span><span class="params">(<span name="a">a: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>, <span name="b">b: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqcmp" data-isabs="false">
      <a id="pqcmp((AlgT, AlgT),(AlgT, AlgT)):Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqcmp</span><span class="params">(<span name="xy">xy: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>, <span name="uv">uv: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqdivide" data-isabs="false">
      <a id="pqdivide((AlgT, AlgT),(AlgT, AlgT)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqdivide</span><span class="params">(<span name="a">a: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>, <span name="b">b: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqinverse" data-isabs="false">
      <a id="pqinverse((AlgT, AlgT)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqinverse</span><span class="params">(<span name="a">a: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqmultiply" data-isabs="false">
      <a id="pqmultiply((AlgT, AlgT),(AlgT, AlgT)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqmultiply</span><span class="params">(<span name="a">a: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>, <span name="b">b: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqop" data-isabs="false">
      <a id="pqop((AlgT, AlgT) ⇒ AlgT,(AlgT, AlgT),(AlgT, AlgT)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqop</span><span class="params">(<span name="f">f: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>) ⇒ <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="xy">xy: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>, <span name="uv">uv: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">addition/subtraction template
</p><div class="fullcomment"><div class="comment cmt"><p>addition/subtraction template
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqsimpl" data-isabs="false">
      <a id="pqsimpl((AlgT, AlgT)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqsimpl</span><span class="params">(<span name="xy">xy: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">simplifies a positive fraction represented as a pair
</p><div class="fullcomment"><div class="comment cmt"><p>simplifies a positive fraction represented as a pair
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#pqsub" data-isabs="false">
      <a id="pqsub((AlgT, AlgT),(AlgT, AlgT)):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">pqsub</span><span class="params">(<span name="a">a: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>, <span name="b">b: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#prime45" data-isabs="false">
      <a id="prime45:Int"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">prime45</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">the prime used as exponent for the largest
known prime number up to december 2012
</p><div class="fullcomment"><div class="comment cmt"><p>the prime used as exponent for the largest
known prime number up to december 2012
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#probablePrimes" data-isabs="false">
      <a id="probablePrimes(AlgT,AlgT):List[AlgT]"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">probablePrimes</span><span class="params">(<span name="from">from: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="k">k: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: List[<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">list of probable primes in the interval  [from,from+k]
</p><div class="fullcomment"><div class="comment cmt"><p>list of probable primes in the interval  [from,from+k]
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#qrand" data-isabs="false">
      <a id="qrand:Random"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">qrand</span><span class="result">: <span name="scala.util.Random" class="extype">Random</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#qtest" data-isabs="false">
      <a id="qtest:Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">qtest</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.Main#r" data-isabs="false">
      <a id="r:AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">r</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      
    </li><li visbl="pub" name="giantnums.GiantRationals#radd" data-isabs="false">
      <a id="radd(Q,Q):Q"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">radd</span><span class="params">(<span name="a">a: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>, <span name="b">b: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#ranA" data-isabs="false">
      <a id="ranA:AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">ranA</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#ranC" data-isabs="false">
      <a id="ranC:giantnums.T.type"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">ranC</span><span class="result">: giantnums.T.type</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#ranM" data-isabs="false">
      <a id="ranM:AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">val</span>
      </span>
      <span class="symbol">
        <span class="name">ranM</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#ranR" data-isabs="false">
      <a id="ranR:AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">var</span>
      </span>
      <span class="symbol">
        <span class="name">ranR</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#random" data-isabs="false">
      <a id="random(AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">random</span><span class="params">(<span name="limit">limit: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">returns a random number between
0 and limit-1
</p><div class="fullcomment"><div class="comment cmt"><p>returns a random number between
0 and limit-1
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#randomN" data-isabs="false">
      <a id="randomN():BigInt"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">randomN</span><span class="params">()</span><span class="result">: BigInt</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#randomQ" data-isabs="false">
      <a id="randomQ():Q"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">randomQ</span><span class="params">()</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#randomT" data-isabs="false">
      <a id="randomT():AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">randomT</span><span class="params">()</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#rat2nat" data-isabs="false">
      <a id="rat2nat(Q):BigInt"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">rat2nat</span><span class="params">(<span name="q">q: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: BigInt</span>
      </span>
      </h4>
      <p class="shortcomment cmt">bijection from tree-represented Signed Rationals to
BigInt natural numbers
</p><div class="fullcomment"><div class="comment cmt"><p>bijection from tree-represented Signed Rationals to
BigInt natural numbers
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#rdivide" data-isabs="false">
      <a id="rdivide(Q,Q):Q"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">rdivide</span><span class="params">(<span name="a">a: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>, <span name="b">b: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#rem" data-isabs="false">
      <a id="rem(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">rem</span><span class="params">(<span name="x">x: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="y">y: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">reminder
</p><div class="fullcomment"><div class="comment cmt"><p>reminder
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#rinverse" data-isabs="false">
      <a id="rinverse(Q):Q with Product with Serializable"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">rinverse</span><span class="params">(<span name="a">a: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a> with <span name="scala.Product" class="extype">Product</span> with <span name="scala.Serializable" class="extype">Serializable</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#rmultiply" data-isabs="false">
      <a id="rmultiply(Q,Q):Q"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">rmultiply</span><span class="params">(<span name="a">a: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>, <span name="b">b: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#ropposite" data-isabs="false">
      <a id="ropposite(Q):Q with Product with Serializable"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">ropposite</span><span class="params">(<span name="x">x: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a> with <span name="scala.Product" class="extype">Product</span> with <span name="scala.Serializable" class="extype">Serializable</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#rsub" data-isabs="false">
      <a id="rsub(Q,Q):Q"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">rsub</span><span class="params">(<span name="a">a: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>, <span name="b">b: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#setSeed" data-isabs="false">
      <a id="setSeed(AlgT):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">setSeed</span><span class="params">(<span name="seed">seed: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">sets the seed of our random generator
</p><div class="fullcomment"><div class="comment cmt"><p>sets the seed of our random generator
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#sub" data-isabs="false">
      <a id="sub(AlgT,AlgT):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">sub</span><span class="params">(<span name="u">u: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>, <span name="v">v: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">subtraction operation on binary trees, corresponding
to subtraction on N
</p><div class="fullcomment"><div class="comment cmt"><p>subtraction operation on binary trees, corresponding
to subtraction on N
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#synchronized" data-isabs="false">
      <a id="synchronized[T0](⇒ T0):T0"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">synchronized</span><span class="tparams">[<span name="T0">T0</span>]</span><span class="params">(<span name="arg0">arg0: ⇒ T0</span>)</span><span class="result">: T0</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#t1" data-isabs="false">
      <a id="t1:Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">t1</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#t2" data-isabs="false">
      <a id="t2:Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">t2</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNaturals#t2n" data-isabs="false">
      <a id="t2n(AlgT):BigInt"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">t2n</span><span class="params">(<span name="t">t: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: BigInt</span>
      </span>
      </h4>
      <p class="shortcomment cmt">converts a tree representation of a natural number
to its bijectively related (non-negative) BigInt representation
</p><div class="fullcomment"><div class="comment cmt"><p>converts a tree representation of a natural number
to its bijectively related (non-negative) BigInt representation
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#t2pq" data-isabs="false">
      <a id="t2pq(AlgT):(AlgT, AlgT)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">t2pq</span><span class="params">(<span name="u">u: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>)</span><span class="result">: (<a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>, <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">splits u seen as a natural number into its
corresponding Calkin-Wilf rational, represented
as a pair
</p><div class="fullcomment"><div class="comment cmt"><p>splits u seen as a natural number into its
corresponding Calkin-Wilf rational, represented
as a pair
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#time" data-isabs="false">
      <a id="time(⇒ Any):Long"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">time</span><span class="params">(<span name="f">f: ⇒ <span name="scala.Any" class="extype">Any</span></span>)</span><span class="result">: <span name="scala.Long" class="extype">Long</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantNumTester#time" data-isabs="false">
      <a id="time:Long"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">time</span><span class="result">: <span name="scala.Long" class="extype">Long</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#toFraq" data-isabs="false">
      <a id="toFraq():(BigInt, BigInt)"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">toFraq</span><span class="params">()</span><span class="result">: (BigInt, BigInt)</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#toString" data-isabs="false">
      <a id="toString():String"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">toString</span><span class="params">()</span><span class="result">: <span name="java.lang.String" class="extype">String</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef → Any</dd></dl></div>
    </li><li visbl="pub" name="giantnums.GiantRationals#toT" data-isabs="false">
      <a id="toT(Q):AlgT"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier"></span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">toT</span><span class="params">(<span name="q">q: <a name="giantnums.Q" class="extype" href="Q.html">Q</a></span>)</span><span class="result">: <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></span>
      </span>
      </h4>
      <p class="shortcomment cmt">From Signed Rationals to trees seen as natural numbers
</p><div class="fullcomment"><div class="comment cmt"><p>From Signed Rationals to trees seen as natural numbers
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#wait" data-isabs="false">
      <a id="wait():Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">wait</span><span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#wait" data-isabs="false">
      <a id="wait(Long,Int):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">wait</span><span class="params">(<span name="arg0">arg0: <span name="scala.Long" class="extype">Long</span></span>, <span name="arg1">arg1: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#wait" data-isabs="false">
      <a id="wait(Long):Unit"></a>
      <h4 class="signature">
      <span class="modifier_kind">
        <span class="modifier">final </span>
        <span class="kind">def</span>
      </span>
      <span class="symbol">
        <span class="name">wait</span><span class="params">(<span name="arg0">arg0: <span name="scala.Long" class="extype">Long</span></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li></ol>
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        <div id="inheritedMembers">
        <div name="giantnums.GiantNumTester" class="parent">
              <h3>Inherited from <a name="giantnums.GiantNumTester" class="extype" href="GiantNumTester.html">GiantNumTester</a></h3>
            </div><div name="giantnums.GiantRationals" class="parent">
              <h3>Inherited from <a name="giantnums.GiantRationals" class="extype" href="GiantRationals.html">GiantRationals</a></h3>
            </div><div name="giantnums.GiantNaturals" class="parent">
              <h3>Inherited from <a name="giantnums.GiantNaturals" class="extype" href="GiantNaturals.html">GiantNaturals</a></h3>
            </div><div name="giantnums.AlgT" class="parent">
              <h3>Inherited from <a name="giantnums.AlgT" class="extype" href="AlgT.html">AlgT</a></h3>
            </div><div name="scala.App" class="parent">
              <h3>Inherited from <span name="scala.App" class="extype">App</span></h3>
            </div><div name="scala.DelayedInit" class="parent">
              <h3>Inherited from <span name="scala.DelayedInit" class="extype">DelayedInit</span></h3>
            </div><div name="scala.AnyRef" class="parent">
              <h3>Inherited from AnyRef</h3>
            </div><div name="scala.Any" class="parent">
              <h3>Inherited from <span name="scala.Any" class="extype">Any</span></h3>
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